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Course Description Our first year liberal arts mathematics course is a survey in breadth rather than depth of a variety of mathematical topics. While emphasis is on the spirit, concepts and structure of modern mathematics, manipulative skills and techniques are also developed. This course is usually the only mathematics course that the students accomplish in their undergraduate studies. The class size varies between 20 to 35 students per section each semester. Usually two sections of this liberal arts mathematics course are offered in the fall semester and one section in the spring semester. One of the spring sections met three times a week for 50 minutes each class period and the other sections met twice a week for 75 minutes each day.
For each semester of the lesson study, classes were taught in technology enhanced classrooms where projection of computer files was available. In spring semester students were arranged in groups at tables and in the fall semester students were provided movable single desks. This also provided an opportunity to work in small groups, but was not as natural as conversing when seated at the same table. The revised version of our lesson utilized digital ink as the teacher collaborated with the students and recorded initial data into a table. This specialized equipment is recommended but could be substituted by an overhead projector and tables prepared on transparencies.
The class atmosphere in each of the sections was congenial, students were comfortable and friendly toward each other and were used to working in small groups and writing about mathematics as well as solving problems.
One component of this course is applications in real contexts (quantitative literacy). This lesson study focused on interest rate models based on applications of linear functions (municipal bonds) and exponential functions (certificates of deposit). This lesson would be the first lesson on the mathematics of financial literacy.
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Executive Summary Our main goal for this lesson is for students to understand the difference between simple interest and compound annual interest. Prerequisite to understanding these concepts is the understanding of the mathematics concepts of rate (interest rate) and percents. A related goal is the recognition of the additive nature of simple interest providing a linear rate of growth (additive sequence) and the multiplicative nature of compound interest providing an exponential rate of growth (geometric sequence). Included in our goals is the ability to represent these relationships in numeric, tabular, and graphical forms. Part of the rationale for this project defined in the fall of 2007 was the recent home foreclosures problem in the U.S. (indicating that individuals did not understand the mathematics perhaps of home loan agreements). Unfortunately, the impact of the foreclosure crises was felt even more strongly a year later during our lesson study with the failure of numerous financial institutions and major losses in the stock market. The recent national interest in financial literacy as it relates to citizens understanding rates, percents, investment, interest earned, and growth relate directly to this lesson study. This first lesson on the mathematics of financial literacy is on simple interest earned in contrast to compound interest earned annually. The investment context first introduced was the additive application of simple interest. Students represented an investment in numeric and tabular form and extended the data by working in small groups using a calculator. This data was also analyzed using its graphical form. The compound interest earned (exponential rate of growth) was studied in the same fashion by small groups of students. Students made longer term predictions as to which form of investment would be best over time. Excel was used to investigate further the impact of longer term investments in contrast to each other. These activities were at an appropriate level and resulted in students analyzing differences between the two types of interest earned both numerically and graphically. By the end of the lesson, students readily recognized the type of interest earned directly from only a graphical representation.
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